7x+x^2=588

Solution for 7x+x^2=588 equation:

7x+x^2=588

We move all terms to the left:

7x+x^2-(588)=0

a = 1; b = 7; c = -588;
Δ = b2-4ac
Δ = 72-4·1·(-588)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-49}{2*1}=\frac{-56}{2}
=-28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+49}{2*1}=\frac{42}{2}
=21
$